Question

If x-1 and x+3 are the factors of x^3-ax^2-13x+b then (a,b)

Answer 1

3 , 15

Step-by-step explanation:

QUESTION :-

If (x-1) and (x+3) are the factors of x³ - ax² - 13x + b, then (a, b) = ?

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SOLUTION :-

Let,

p(x) = x³ - ax² - 13x + b

And,

x - 1 = 0

=> x = 1

Now,

put the value of x in p(x), it must be equal to 0

=> p(1) = (1)³ - a(1)² - 13(1) + b = 0

= 1 - a(1) - 13 + b = 0

= - a - 12 + b = 0

= -a + b = 12.....(1)

Again,

x + 3 = 0

=> x = - 3

Put the value of x in p(x) = 0

=> p(-3) = (-3)³ - a(-3)² - 13(-3) + b = 0

= - 27 - a(9) + 39 + b = 0

= - 9a + 12 + b = 0

= - 9a + b = - 12.....(2)

______________________

Then,

Subtract (2) from (1),

=>

- a + b = 12

– -9a + b = - 12

+ - +

=> 8a = 24

=> a = 24÷8

=> a = 3

Now,

put the value of 'a' in (1)

=> - a + b = 12

=> -3 + b = 12

=> b = 12+3

=> b = 15

_____________________

So,

a = 3

b = 15

(a , b) = (3 , 15)

Hope it helps.

#BeBrainly :-)